A linear regression was performed on a bivariate data set with variables x and y. Analysis by a computer software package included the following outpu

Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
-positive
-negative
-zero
b. If the data is IQ test scores, an individual with a negative z-score would have a
-high IQ
-low IQ
-average IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
-watch very little TV
-watch a lot of TV
-watch the average amount of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
-positive
-negative
-zero

There's a roll with 40 coins. A coin officially weighs 5g. The actual weight may be 0.194g off. The roll itself weighs 1.5g. What is the range of possible wights for the roll?

Three Questions on Interpreting the Outcome of the Probability Density Function
I have three questions: What is the interpretation of the outcome of the Probability Density Function (PDF) at a particular point? How is this result related to probability? What we exactly do when we maximize the likelihood?
To better explain my questions:
(i) Consider a continuous random variable X with a normal distribution such that $\mu =1.5$ and ${\sigma }^2=2$. If we evaluate the PDF at a particular point, say 3.4, using the formula:
$f(X)=\frac{1}{\sqrt{2\pi {\sigma }^2}}{e}^{\frac{-{\left(X-\mu \right)}^2}{2{\sigma }^2}},$
we get $f(3.4)=0.1144$. How we interpret this value?
(ii) I previously read that the result of 0.1144 is not necessarily the probability that X takes the value of 3.4. But how the result is related to probability concept?
(iii) Consider a sample of the continuous random variable X of size N=2.5, such that $X_1=2$ and $X_2=3.5$. We can use this sample to maximize the log-likelihood:
$max\ln L(\mu ,\sigma |X_1,X_2)=\ln f(X_1)+\ln f(X_2)$
If f(X) is not exactly a probability, what are we maximizing? Some texts detail that "we are maximizing the probability that a model (set of parameters) reproduces the original data". Is this phrase incorrect?

Intuition of information theory
I am reading the book "Elements of Information Theory" by Cover and Thomas and I am having trouble understanding conceptually the various ideas.
For example, I know that H(X) can be interpreted as the average encoding length. But what does $H(Y|X)$ intuitively mean?
And what is mutual information? I read things like "It is the reduction in the uncertainty of one random variable due to the knowledge of the other". This doesn't mean anything to me as it doesn't help me explain in words why $I(X;Y)=H(Y)-H(Y|X)$. Or explain the chain rule for mutual information.
I also encountered the Data processing inequality explained as something that can be used to show that no clever manipulation of the data can improve the inferences that can be made from the data. $I(X;Y)\ge I(X;Z)$. If I had to explain this result to someone in words and explain why it should be intuitively true I would have absolutely no idea what to say. Even explaining how "data processing" is related to a markov chains and mutual information would baffle me.
I can imagine explaining a result in algebraic topology to someone since there is usually an intuitive geometric picture that can be drawn. But with information theory if I had to explain a result to someone at comparable level to a picture I would not be able to.
When I do problems its just abstract symbolic manipulations and trial and error. I am looking for an explanation (not these blah gives information about blah explanations) of the various terms that will make the solutions to problems appear in a meaningful way.
Right now I feel like someone trying to do algebraic topology purely symbolically without thinking about geometric pictures.
Is there a book that will help my curse?

Interpreting Normal Quantite Plots. In Exercises 5–8, examine the normal quantite plot and determine whether the sample data appear to be from a population with a normal distribution.
Dunkin’ Donuts Service Times The normal quantile plot represents service times during the dinner hours at Dunkin’ Donuts (from Data Set 25 “Fast Food” in Appendix B).

Maria's Pizza sells one 16-inch cheese pizza or two 10-inch cheese pizzas for $9.99. Determine which size given more pizza.

Replacement of paint on highways and streets represents a large investment of funds by state and local governments each year. A new, cheaper brand of paint is tested for durability after one month’s time by reflectometer readings. For the new brand to be acceptable, it must have a mean reflectometer reading greater than 19.6. The sample data, based on 35 randomly selected readings, show $x=19.8ands=1.5$. Do the sample data provide sufficient evidence to conclude that the new brand is acceptable? Conduct hypothesis test using $a=.05$. Use the traditional approach and the p-value approach to hypothesis testing! Show all of the steps of the hypothesis test for each approach.